This is too broad a topic to answer directly.
If you are at the beginner stage with neural networks, you will need to learn some basic theory of the maths of neural networks, before the code will make sense. Although it is possible to write neural network code with only a vague understanding of what is going on, it is not a great way to learn for the future, and more advanced neural network features will likely remain beyond your comprehension.
The maths for back propagation are not that difficult conceptually, it is literally just the Chain Rule from basic calculus applied repeatedly. You do this to get a gradient that tells you the direction that an error function would increase in, then take a small step in the opposite direction. Repeat this over time and the error should reduce.
Despite the simplicity once you already know it, there are a lot of moving parts to training a neural network. The formulae for back propagation include multiple symbols with different meanings, and typically indexed in at least 3 dimensions all at once. It can look like a wall of impenetrable maths, especially if you have got a bit rusty at basic calculus and matrix multiplication, and need to review it.
The answer is to take your time and study the basics carefully. There are many resources out there. Introductory material should cover:
Revision of basic linear algebra. Just vectors, matrices and how to add and multiply them.
Revision of basic calculus. Just differentiation and gradients. The chain rule is handy for later.
Linear regression and logistic regression models trained using gradient descent. These are introductory models that naturally lead to layered neural networks.
Neural networks and back propagation.
There are many courses and books that attempt to teach you these things. It is hard to say in general which one would work best for a particular student. The best thing to do would be to go to a learning resource that you already like, such as Coursera or EDX, and search for "neural networks beginner" or similar.
Here are a couple of courses that I can personally recommend. I cannot create a comprehensive list, so if these do not apply on a quick browse (or if the links finally go stale after a few years), then you should search for something more suitable bearing in mind the syllabus suggestions above:
Andrew Ngs' Machine Learning covers more than just neural networks, but the extra parts apply to other aspects of ML, such as sensible approaches to validating and testing that anyone building predictive models should get to know. Code exercises are in Matlab or Octave.
Andrew Ngs' Introduction to Deep Learning starts with basic regression, and moves very quickly to practical builds of neural networks using TensorFlow. It is part of a five course "Specialisation" that works up to advanced NN models developed in the last three years.
Geoffrey Hinton's Neural Networks for Machine Learning covers some historical models (such as perceptrons) and some more obscure models, and the material is hard to understand, but quite rewarding if you are up to it. Not generally recommended to beginners, but if you have solid maths and computing knowledge already, at degree level, but never looked at a neural network before, this might be the right style of course for you.
They all happen to be Coursera courses . . . I am not affiliated, it is just that the relevant courses that I have personally taken have been on that platform.
